I earned this achievement at the beginning of the game, during the "Flaming Joe's" quest, where you're tasked with putting out the fire at the inn.
The point of this puzzle is to match up as many blues while matching up as few reds as possible. Being so early in the game, the board is slanted heavily in your favor. Take your time, plan your moves, and you will should able to get 4 and 5 in a row very easily.
Good tips from the comments:
-Set it to easy, this will drop the health of the fire to merely 25.
-If you accidentally end your turn before defeating the fire, you can hit Start and Quit to quit the battle. This will only take you out of the fight, not back to the main menu. From here, you can easily re-start the fire battle.